This article is what I was about to post when I had made the
bad choice of responding instead to Axel's positions, enticed
by his misleading "hints" about "score".

In one of my previous posts, I had written:

https://groups.google.com/g/rec.games.backgammon/c/lcOpsz6CJgk/m/Ad5tFc0lBAAJ

On March 6, 2023 at 3:29:23 AM UTC-7, MK wrote:

>> XGID=-ABbBCC-B----a---bbbbBbb--:0:0:1:54:0:0:3:0:10
>> X to play 54

> I spent over half hour trying all kinds of combinations of
> match lengths and match scores and cube values to see
> if Ex-Gee would make a move other than 6/1 5/1.

> In all that time, I came accross only a few match lengths
> and match scores and cube values combinations that
> Ex-Gee actually played 21/16 5/1.

> As you may have guesses, I was clueless as to what caused
> Ex-Gee to play anything other than 6/1 5/1 in those situations.

> For now, I won't share those situations with you here in order
> to see if anyone of you can come up with similar examples
> and/or if any of the AI-bot developers here can directly give
> any explanations based on their having programmed some
> algorithms into their gamblegammon bots.

Nobody posted any examples or formulas since then but
Axel's explaining his "hints" (as not about score because
his examples didn't have "lop-sided scores" and the cube
values weren't "high"), indicates that he must have at least
experimented with different scores/cubes even if he hasn't
posted about them.

Indeed, in the subject position above, the bots make "bold"
moves only if the score is very lop-sided and if at the same
time the cube is high enough but not too high (kind of in a
"Goldilocks Zone").

Before starting to talk about matches, let me reiterate that
the "54 safe or bold?" was a stupid question to ask for the
money game example position and sure enough both Ex-Gee
and Noo-BG always play 6/1 5/1 regardless of with/without
jacoby, cube value, cube ownership and equity.

Since I'm clueless about estimating equities, cubing points,
MET's, etc. I had to experiment by poking around. I tried score
and cube combinations in matches from 7 to 33 points, but
focused most on 15 and 25 matches. Here are my generalized
observations with some actual examples, following which I will
make a few final comments.

All examples with both bots using Rockwell/Kazaross MET
but Noo-BG played the same positions somewhat differently.

(Notice that Noo-BG allows centered cube values > 1 and it
analyzes them as though the player to move owns the cube.)

With the cube at 1, 2, 4, 32, 64, ... owned by either side, both
Noo-BG and Ex-Gee always played 6/1 5/1 at any score and
at any match length.

With the cube at 8, owned by either side, both Noo-BG and
Ex-Gee played 6/1 5/1 or 21/16 5/1 or 21/12 or 8/4 6/1
depending on score and match length combinations.

With the cube at 16, owned by either side, Ex-Gee played
6/1 5/1 or 21/16 5/1 or 21/12 or 8/4 6/1 depending on the
score and match length combinations, but Noo-BG always
played 6/1 5/1.

Here are some Ex-Gee examples with cube at 16:

XGID=-ABbBCC-B----a---bbbbBbb--:4:1:1:54:2:22:0:25:10
MWC: 24.122% P: 51.3 6.1 0.1 - O: 48.7 8.5 0.2
At score X=2, O=22 it plays 6/1 5/1

XGID=-ABbBCC-B----a---bbbbBbb--:4:1:1:54:1:22:0:25:10
MWC: 20.478% P: 42.1 6.9 0.1 - O: 57.9 9.4 0.3
At score X=1, O=22 it plays 8/4 6/1

XGID=-ABbBCC-B----a---bbbbBbb--:4:1:1:54:0:22:0:25:10
MWC: 17.720% P: 46.9 6.7 0.1 - O: 53.1 11.1 0.4
At score X=0, O=22 it plays 21/12

XGID=-ABbBCC-B----a---bbbbBbb--:4:1:1:54:0:21:0:25:10
MWC: 21.949% P: 42.0 7.0 0.1 - O: 58.0 9.4 0.3
At score X=0, O=21 it plays 8/4 6/1

Here are some Ex-Gee examples with cube at 8:

XGID=-ABbBCC-B----a---bbbbBbb--:3:1:1:54:2:22:0:25:10
MWC: 4.870% P: 48.9 6.3 0.1 - O: 51.1 10.5 0.4
At score X=2, O=22 it plays 21/12

XGID=-ABbBCC-B----a---bbbbBbb--:3:1:1:54:1:22:0:25:10
MWC: 3.983% P: 50.6 6.3 0.1 - O: 49.4 9.8 0.4
At score X=1, O=22 it plays 21/12

XGID=-ABbBCC-B----a---bbbbBbb--:3:1:1:54:0:22:0:25:10
MWC: 3.224% P: 51.0 6.2 0.1 - O: 49.0 9.7 0.4
At score X=0, O=22 it plays 21/12

XGID=-ABbBCC-B----a---bbbbBbb--:3:1:1:54:0:21:0:25:10
MWC: 4.733% P: 42.1 6.9 0.1 - O: 57.9 9.3 0.3
At score X=0, O=21 it plays 8/4 6/1

Here are some Noo-BG examples with cube at 16:

GNUbg ID: NtuGAAzN7gwABg:VIkyA2ABEAAA
MWC: 25.08%
At score X=2, O=22 it plays 8/4 6/1

GNUbg ID: NtuGAAzN7gwABg:VIkyA2ABCAAA
MWC: 22.01%
At score X=1, O=22 it plays 8/4 6/1

GNUbg ID: NtuGAAzN7gwABg:VIkyA2ABAAAA
MWC: 19.35%
At score X=0, O=22 it plays 21/12

GNUbg ID: NtuGAAzN7gwABg:VIkyA1ABAAAA
MWC: 23.28%
At score X=0, O=21 it plays 8/4 6/1

Here are some Noo-BG examples with cube at 8:

GNUbg ID: NtuGAAzN7gwABg:U4kyA2ABEAAA
MWC: 5.33%
At score X=2, O=22 it plays 21/16 5/1

GNUbg ID: NtuGAAzN7gwABg:U4kyA2ABCAAA
MWC: 4.34%
At score X=1, O=22 it plays 21/16 5/1

GNUbg ID: NtuGAAzN7gwABg:U4kyA2ABAAAA
MWC: 3.54%
At score X=0, O=22 it plays 21/16 5/1

GNUbg ID: NtuGAAzN7gwABg:U4kyA1ABAAAA
MWC: 5.12%
At score X=0, O=21 it plays 21/16 5/1

Obviously the bots use the same/similar fancifully elaborate
formulas to calculate the MWC's using the MET's, in order to
precisely pick the best moves.

How could I not be totally impressed by the above garbage
produced by Ex-Gee and Noo-BG...? :)

What I can't figure out though is whether the scores need to
be so highly lop-sided in addition to and in relation to high
"Goldilocks cube values", or the formulaes themselves are
lop-sided...?? :(

MK